# TwoPortOnePath, EnhancedResponse, and FakeFlip

## Intro

This example demonstrates a macgyver-ish shortcut you can take if you are measuring a device that is ** reciprocal** and **symmetric** on a switch-less three-receiver system. For more information about error correction this type of architecture, see Calibration With Three Receivers.

In general, full error correction of a 2-port network on a switchless three-receiver architecture requires each DUT to measured in two orientations. However, if the DUT is known to be reciprocal (\(S_{21}=S_{12}\)) and symmetric (\(S_{11}=S_{22}\)), then measurements in both orientations produce the same response, and therefore are unnecessary.

The following worked example compares the corrected response of a 10dB attenuator at WR-12 as corrected using full error correction and pseudo-full error correction using:

Full Correction

Pseudo-Full Correction (FakeFlip)

Partial (EnhancedResponse)

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```
from IPython.display import Image
Image('three_receiver_cal/pics/macgyver.jpg', width='50%')
```

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## Example

These measurements where taken on a Agilent PNAX with a set of VDI WR-12 TXRX-RX Frequency Extender heads. The measurements of the calibration standards and DUT’s were downloaded from the VNA by saving touchstone files of the raw s-parameter data to disk.

In the code that follows a TwoPortOnePath calibration is created from corresponding measured and ideal responses of the calibration standards. The measured networks are read from disk, while their corresponding ideal responses are generated using scikit-rf. More information about using scikit-rf to do offline calibrations can be found here.

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```
import matplotlib.pyplot as plt
import skrf as rf
%matplotlib inline
from skrf import mil
from skrf import two_port_reflect as tpr
from skrf.calibration import TwoPortOnePath
from skrf.media import RectangularWaveguide
rf.stylely()
raw = rf.read_all_networks('three_receiver_cal/data/')
# pull frequency information from measurements
frequency = raw['short'].frequency
# the media object
wg = RectangularWaveguide(frequency=frequency, a=120*mil, z0_override=50)
# list of 'ideal' responses of the calibration standards
ideals = [wg.short(nports=2),
tpr(wg.delay_short( 90,'deg'), wg.match()),
wg.match(nports=2),
wg.thru()]
# corresponding measurements to the 'ideals'
measured = [raw['short'],
raw['quarter wave delay short'],
raw['load'],
raw['thru']]
# the Calibration object
cal = TwoPortOnePath(measured = measured, ideals = ideals )
```

```
/home/docs/checkouts/readthedocs.org/user_builds/scikit-rf/checkouts/latest/.venv/lib/python3.10/site-packages/skrf/calibration/calibration.py:1912: UserWarning: n_thrus is None, guessing which stds are transmissive
TwelveTerm.__init__(self,*args, **kwargs)
```

## Correction Options

With the calibration created above, we compare the corrected response of WR-12 10dB attenuator using **Full**, **Pseudo-Full**, and **Partial** Correction. Each correction algorithm is described below.

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```
Image('three_receiver_cal/pics/symmetric DUT.jpg', width='75%')
```

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### Full Correction (TwoPortOnePath)

Full correction on this type of architecture has been called *TwoPortOnePath*. In `scikit-rf`

using this correction algorithm requires the device to be measured in both orientations, **forward** and **reverse**, and passing them both to the `apply_cal()`

function as a `tuple`

. Neglecting the connector uncertainty, this type of correction is identical to full two-port **SOLT** calibration.

### Pseudo-full Correction ( FakeFlip)

If we assume the DUT is **reciprocal** and **symmetric**, then measuring the device in both orientations will produce the same result. Therefore, the reverse orientation measurement may be replaced by a copy of the forward orientation measurement. We refer to this technique as the *Fake Flip*.

**Warning**: Be sure that you understand the assumptions of reciprocity and symmetry before using this macgyver technique, incorrect usage can lead to nonsense results.

### Partial Correction (EnhancedResponse)

If you pass a single measurement to the `apply_cal()`

function, then the calibration will employ partial correction. This type of correction is known as `EnhancedResponse`

. While the *Fake Flip* technique assumes the device is reciprocal and symmetric, the `EnhancedResponse`

algorithm *implicitly* assumes that the port 2 of the device is perfectly matched. The accuracy of the corrected result produced with either of these algorithms depends on accuracy of the assumptions.

## Comparison

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```
dutf = raw['attenuator (forward)']
dutr = raw['attenuator (reverse)']
# note the correction algorithm is different depending on what is passed to
# apply_cal
corrected_full = cal.apply_cal((dutf, dutr))
corrected_fakeflip = cal.apply_cal((dutf,dutf))
corrected_partial = cal.apply_cal(dutf)
f, ax = plt.subplots(2,2, figsize=(8,8))
for m in [0,1]:
for n in [0,1]:
ax_ = ax[m,n]
ax_.set_title('$S_{%i%i}$'%(m+1,n+1))
corrected_full.plot_s_db(m,n, label='Full Correction',ax=ax_ )
corrected_fakeflip.plot_s_db(m,n, label='Pseudo-full Correction', ax=ax_)
if n==0:
corrected_partial.plot_s_db(m,n, label='Partial Correction', ax=ax_)
plt.tight_layout()
```

```
/tmp/ipykernel_4753/1466338557.py:9: UserWarning: only gave a single measurement orientation, error correction is partial without a tuple
corrected_partial = cal.apply_cal(dutf)
/home/docs/checkouts/readthedocs.org/user_builds/scikit-rf/checkouts/latest/.venv/lib/python3.10/site-packages/skrf/mathFunctions.py:268: RuntimeWarning: divide by zero encountered in log10
out = 20 * np.log10(z)
```

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